Effective Potential for Scalar Field in Three Dimensions: Ising Model in the Ferromagnetic Phase

الأصل · EN

We compute the effective potential V eff(ϕ) for one-component real scalar field ϕ in three Euclidean dimensions (3D) in the case of spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising model in external field at temperatures approaching the phase transition from below. We study probability distributions of the order parameter on the lattices from 30³ to 74³, at L/ξ≈ 10. We find that, in close analogy with the symmetric case, ϕ⁶ plays an important role: V eff(ϕ) is very well approximated by the sum of ϕ², ϕ⁴ and ϕ⁶ terms. An unexpected feature is the negative sign of the ϕ⁴ term. As close to the continuum limit as we can get (ξ≈ 7.2), we obtain L eff ≈ 1 2 ∂μϕ∂μϕ+ 1.7 (ϕ² - η²)² (ϕ² + η²). We also compute several universal coupling constants and ratios, including the combination of critical amplitudes C- (f₁-)⁻³ B⁻².